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          微信一笔画完小游戏的解题算法
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        <p>前一阵子事情比较杂，因此停了很久才来更新博客。</p>
<p>最近在微信看到一个一笔画完的小游戏，大概规则是，在一个长方形的地图上，只画一笔遍历所有可达点。于是我用递归的思路，使用python写出了解题算法。</p>
<p>小游戏的截图：<br><img src="http://imgs.maotoumao.xyz/57089349-daeae700-6d36-11e9-8706-6d765129e2a2.jpg" alt="base_img"></p>
<p>算法思路如下：</p>
<p>地图可以表示为一个矩阵map，这个矩阵中，0表示该位置不可达，1则表示该位置是可达的。特殊地，初始点所在的位置记为1。</p>
<p>除此之外，我们需要一个与map相同大小的矩阵，来记录当前的位置是否被访问过。</p>
<p>接下来，我们用递归的思路去解决这个问题。<br>从初始点开始，每一个位置都有四种可能的方向。我们循环对这四种方向进行尝试，即从一个新的点去继续搜索，直至搜索不到返回false或者返回一个操作序列。</p>
<p>代码如下：<br><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">OneLine</span>(<span class="params"><span class="built_in">object</span></span>):</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__init__</span>(<span class="params">self, row, col</span>):</span></span><br><span class="line">        <span class="string">&#x27;&#x27;&#x27;</span></span><br><span class="line"><span class="string">        map 是原地图 0表示位置不可用，1表示可用</span></span><br><span class="line"><span class="string">        status 表示已经访问过的点，1表示未访问，0表示已访问</span></span><br><span class="line"><span class="string">        :param row: 行</span></span><br><span class="line"><span class="string">        :param col: 列</span></span><br><span class="line"><span class="string">        &#x27;&#x27;&#x27;</span></span><br><span class="line">        self.<span class="built_in">map</span> = np.zeros((row, col))</span><br><span class="line">        self.status = np.ones((row, col))</span><br><span class="line">        self.init = <span class="literal">None</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">set_position_available</span>(<span class="params">self, x, y</span>):</span></span><br><span class="line">        self.<span class="built_in">map</span>[x][y] = <span class="number">1</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">set_map</span>(<span class="params">self, <span class="built_in">map</span></span>):</span></span><br><span class="line">        self.<span class="built_in">map</span> = <span class="built_in">map</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">set_init_point</span>(<span class="params">self, point</span>):</span></span><br><span class="line">        self.init = point</span><br><span class="line">        self.status[point[<span class="number">0</span>], point[<span class="number">1</span>]] = <span class="number">0</span></span><br><span class="line">        self.state = self.<span class="built_in">map</span> * self.status</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">is_finished</span>(<span class="params">self, state</span>):</span></span><br><span class="line">        <span class="keyword">if</span> (np.<span class="built_in">sum</span>(state) == <span class="number">0</span>):</span><br><span class="line">            <span class="keyword">return</span> <span class="literal">True</span></span><br><span class="line">        <span class="keyword">else</span>:</span><br><span class="line">            <span class="keyword">return</span> <span class="literal">False</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">move_to</span>(<span class="params">self, <span class="built_in">map</span>, status, curr_point, op_code</span>):</span></span><br><span class="line">        next_status = copy.copy(status)</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (op_code == <span class="string">&#x27;r&#x27;</span>):  <span class="comment"># 右划</span></span><br><span class="line">            next_point = [curr_point[<span class="number">0</span>], curr_point[<span class="number">1</span>] + <span class="number">1</span>]</span><br><span class="line">        <span class="keyword">elif</span> (op_code == <span class="string">&#x27;l&#x27;</span>):  <span class="comment"># 左划</span></span><br><span class="line">            next_point = [curr_point[<span class="number">0</span>], curr_point[<span class="number">1</span>] - <span class="number">1</span>]</span><br><span class="line">        <span class="keyword">elif</span> (op_code == <span class="string">&#x27;u&#x27;</span>):  <span class="comment"># 上划</span></span><br><span class="line">            next_point = [curr_point[<span class="number">0</span>] - <span class="number">1</span>, curr_point[<span class="number">1</span>]]</span><br><span class="line">        <span class="keyword">elif</span> (op_code == <span class="string">&#x27;d&#x27;</span>):  <span class="comment"># 下划</span></span><br><span class="line">            next_point = [curr_point[<span class="number">0</span>] + <span class="number">1</span>, curr_point[<span class="number">1</span>]]</span><br><span class="line">        <span class="keyword">else</span>:</span><br><span class="line">            next_point = curr_point</span><br><span class="line"></span><br><span class="line">        next_status[next_point[<span class="number">0</span>], next_point[<span class="number">1</span>]] = <span class="number">0</span></span><br><span class="line">        next_state = <span class="built_in">map</span> * next_status</span><br><span class="line">        <span class="keyword">return</span> &#123;<span class="string">&#x27;map&#x27;</span>: <span class="built_in">map</span>, <span class="string">&#x27;status&#x27;</span>: next_status, <span class="string">&#x27;state&#x27;</span>: next_state, <span class="string">&#x27;curr_point&#x27;</span>: next_point&#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">get_available_operation</span>(<span class="params">self, state, curr_point</span>):</span></span><br><span class="line">        op_list = []</span><br><span class="line">        dim = state.shape</span><br><span class="line">        <span class="keyword">if</span> (curr_point[<span class="number">0</span>] &gt; <span class="number">0</span> <span class="keyword">and</span> state[curr_point[<span class="number">0</span>] - <span class="number">1</span>, curr_point[<span class="number">1</span>]] == <span class="number">1</span>):</span><br><span class="line">            op_list.append(<span class="string">&#x27;u&#x27;</span>)</span><br><span class="line">        <span class="keyword">if</span> (curr_point[<span class="number">0</span>] &lt; dim[<span class="number">0</span>] - <span class="number">1</span> <span class="keyword">and</span> state[curr_point[<span class="number">0</span>] + <span class="number">1</span>, curr_point[<span class="number">1</span>]] == <span class="number">1</span>):</span><br><span class="line">            op_list.append(<span class="string">&#x27;d&#x27;</span>)</span><br><span class="line">        <span class="keyword">if</span> (curr_point[<span class="number">1</span>] &gt; <span class="number">0</span> <span class="keyword">and</span> state[curr_point[<span class="number">0</span>], curr_point[<span class="number">1</span>] - <span class="number">1</span>] == <span class="number">1</span>):</span><br><span class="line">            op_list.append(<span class="string">&#x27;l&#x27;</span>)</span><br><span class="line">        <span class="keyword">if</span> (curr_point[<span class="number">1</span>] &lt; dim[<span class="number">1</span>] - <span class="number">1</span> <span class="keyword">and</span> state[curr_point[<span class="number">0</span>], curr_point[<span class="number">1</span>] + <span class="number">1</span>] == <span class="number">1</span>):</span><br><span class="line">            op_list.append(<span class="string">&#x27;r&#x27;</span>)</span><br><span class="line">        <span class="keyword">return</span> op_list</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">search_path</span>(<span class="params">self, <span class="built_in">map</span>, status, state, curr_point, path</span>):</span></span><br><span class="line">        <span class="comment"># 如果找到解，返回</span></span><br><span class="line">        <span class="keyword">if</span> (self.is_finished(state)):</span><br><span class="line">            <span class="keyword">return</span> path</span><br><span class="line">        <span class="comment"># 否则进行尝试</span></span><br><span class="line">        available_op = self.get_available_operation(state, curr_point)</span><br><span class="line">        <span class="comment"># 如果当前没走到死路</span></span><br><span class="line">        <span class="keyword">while</span> (<span class="built_in">len</span>(available_op) != <span class="number">0</span>):</span><br><span class="line">            op = available_op.pop()</span><br><span class="line">            mov = self.move_to(<span class="built_in">map</span>, status, curr_point, op)</span><br><span class="line">            path.append(op)</span><br><span class="line">            p = self.search_path(mov[<span class="string">&#x27;map&#x27;</span>], mov[<span class="string">&#x27;status&#x27;</span>], mov[<span class="string">&#x27;state&#x27;</span>], mov[<span class="string">&#x27;curr_point&#x27;</span>], path)</span><br><span class="line">            <span class="keyword">if</span> (p != <span class="literal">False</span>):</span><br><span class="line">                <span class="keyword">return</span> p</span><br><span class="line">        path.pop()</span><br><span class="line">        <span class="keyword">return</span> <span class="literal">False</span></span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">start_find</span>(<span class="params">self</span>):</span></span><br><span class="line">        <span class="keyword">return</span> self.search_path(self.<span class="built_in">map</span>, self.status, self.state, self.init, [])</span><br><span class="line"></span><br><span class="line"></span><br></pre></td></tr></table></figure></p>
<p><a target="_blank" rel="noopener" href="https://github.com/Stranger-97/one_line_helper/">完整代码指路github</a></p>

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